TURUNAN DAN DIFERENSIASI

MUHAMMAD FAQIH 2022-11-30 NAMA MAHASISWA : MUHAMMAD FAQIH

NIM : 220605110069

MATA KULIAH : KALKULUS

DOSEN PENGAMPU : Prof. Dr. Suhartono, M.Kom

JURUSAN : TEKNIK INFORMATIKA

UNIVERSITAS : UIN MAULANA MALIK IBRAHIM MALANG

TURUNAN DAN DIFERENSIASI

================================================================================ Turunan fungsi (diferensial) ialah fungsi lain dari suatu fungsi sebelumnya, misalnya fungsi f menjadi f’ yang memiliki nilai tak beraturan. Turunan (diferensial) dipakai sebagai suatu alat untuk menyelesaikan berbagai masalah dalam geometri dan mekanika.

Input: ekspresi menggunakan ~notasi. Contoh: x^2~xatau sin(x^2)~xatauy*cos(x)~y

library(mosaicCalc)

## Loading required package: mosaic

## Registered S3 method overwritten by 'mosaic':
##   method                           from   
##   fortify.SpatialPolygonsDataFrame ggplot2

## 
## The 'mosaic' package masks several functions from core packages in order to add 
## additional features.  The original behavior of these functions should not be affected by this.

## 
## Attaching package: 'mosaic'

## The following objects are masked from 'package:dplyr':
## 
##     count, do, tally

## The following object is masked from 'package:Matrix':
## 
##     mean

## The following object is masked from 'package:ggplot2':
## 
##     stat

## The following objects are masked from 'package:stats':
## 
##     binom.test, cor, cor.test, cov, fivenum, IQR, median, prop.test,
##     quantile, sd, t.test, var

## The following objects are masked from 'package:base':
## 
##     max, mean, min, prod, range, sample, sum

## Loading required package: mosaicCore

## 
## Attaching package: 'mosaicCore'

## The following objects are masked from 'package:dplyr':
## 
##     count, tally

## 
## Attaching package: 'mosaicCalc'

## The following object is masked from 'package:stats':
## 
##     D

g <- D(x^2 ~ x)
g(1)

## [1] 2

g(3.5)

## [1] 7

Untuk ekspresi input lainnya, D()akan mengembalikan fungsi yang didasarkan pada perkiraan numerik ke turunan

Sebagai Contoh :

h <- D(sin(abs(x - 3) ) ~ x)
h

## function (x) 
## {
##     .e1 <- x - 3
##     cos(abs(.e1)) * sign(.e1)
## }

’

Parameter Simbolik –>

Kita dapat menyertakan parameter simbolik dalam ekspresi yang dimasukkan ke D()

Contoh :

s2 <- D(A  * sin(2 * pi * t / P) + C ~ t)
s2

## function (t, A, C, P) 
## (2 * A * pi * cos((2 * pi * t)/P))/P

library(mosaicCalc)
slice_plot(s2(t, A=2, P=10, C=4) ~ t, 
           domain(t=range(0,20)), color = "red")

REFERENCES

https://rpubs.com/ekamiraa/839987#:~:text=Lalu%20apa%20yang%20dimaksud%20dengan,masalah%20dalam%20geometri%20dan%20mekanika. https://dtkaplan.github.io/RforCalculus/fitting-functions-to-data.html#curves-and-linear-models